Date: June 2017Source: Biological Shape Analysis: Proceedings of the 4th International Symposium (ISBSA), pp 249-258. School of Dentistry, UCLA, USA, 19–22 June 2015.Abstract: Facial morphology is the result of mazy interactions between environmental and epigenetic factors that lead to the composition of multiple subunits integrated to function as a whole. In this work, we combine modularity concepts from evolutionary developmental biology with unsupervised machine learning tools to provide a descriptive framework of the facial configuration of landmarks on a modular basis. We apply normalized spectral clustering to a database of 592 3D faces – represented with spatially dense meshes of 7,150 quasi-landmarks – grouping vertices that are strongly correlated and connected to form compact modules. We first build the affinity matrix that encodes the structural similarity, both in terms of correlation and distance, between each pair of landmarks. The normalized spectral clustering is then applied on the affinity matrix built as such. Since the strength of co-variation between the obtained modules is the criterion for evaluating integration and modularity in the input data, we recall on the Escoufier coefficient from morphometric studies on biological shapes, as a scalar measure of the covariation between sets of landmarks. Statistical significance of the Escoufier coefficients among multiple sets of landmarks is established by means of a permutation test that is extended to 3D spatially dense landmark data. The spectral clustering described in this work results in finding the correct patterns in a more robust and accurate way compared to other unsupervised clustering techniques such as k-means or k-means++.